Hyperkähler cones and instantons on quaternionic Kähler manifolds

Abstract

AbstractWe present a novel approach to the study of Yang–Mills instantons on quaternionic Kähler manifolds, based on an extension of the harmonic space method of constructing instantons on hyperkähler manifolds. Our results establish a bijection between local equivalence classes of instantons on quaternionic Kähler manifolds M and equivalence classes of certain holomorphic maps on an appropriate $${\mathrm {SL}}_2({\mathbb {C}})$$ SL 2 ( C ) -bundle over the Swann bundle of M.